Fundamental properties of the proton in light-front zero modes

For a proton in the infinite momentum frame, its wave function contains a zero-momentum part (light-front zero-modes) originated from the modification of the QCD vacuum in the presence of the valence quarks, exhibiting a light-front long-range order in the quantum state. This “non-travelling” component of the proton contributes to its fundamental properties, including the mass and spin, as well as the naive-time-reversal-odd correlations between transverse momentum and spin. The large momentum effective theory (LaMET) provides a theoretical approach to study the physical properties of the proton's zero-mode “condensate” through lattice simulations.